Operator.h 106 KB
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     */
    BinaryAbstractFunction<WorldMatrix<double>, 
			   double, WorldVector<double> > *f;
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    AbstractFunction<WorldVector<double>, WorldMatrix<double> > *divFct;
    
    /** \brief
     * Pointer to a WorldVector<double> array containing the gradients of the DOFVector
     * at each quadrature point.
     */
    double* vecAtQPs;
    WorldVector<double>* gradAtQPs;
    
    bool symmetric;
  };
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  /**
   * \ingroup Assembler
   *
   * \brief
   * Laplace multiplied with a function which maps the gradient of a DOFVector
   * at each quadrature point to a double:
   * \f$ f(\nabla v(\vec{x})) \Delta u(\vec{x}) \f$
   */
  class VecGradCoordsAtQP_SOT : public SecondOrderTerm
  {
  public:
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    /// Constructor.
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    VecGradCoordsAtQP_SOT(DOFVectorBase<double> *dv,
			  TertiaryAbstractFunction<double, double,
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			  WorldVector<double>, WorldVector<double> > *af);
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements SecondOrderTerm::getLALt().
     */
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    void getLALt(const ElInfo *elInfo, int nPoints, DimMat<double> **LALt) const;
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    /** \brief
     * Implenetation of SecondOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

    /** \brief
     * Implenetation of SecondOrderTerm::weakEval().
     */
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    void weakEval(int nPoints,
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		  const WorldVector<double> *grdUhAtQP,
		  WorldVector<double> *result) const;

  protected:
    DOFVectorBase<double>* vec;

    /** \brief
     * Function wich maps \ref gradAtQPs to a double.
     */
    TertiaryAbstractFunction<double, double, WorldVector<double>,
			     WorldVector<double> > *f;

    /** \brief
     * Pointer to a WorldVector<double> array containing the gradients of the DOFVector
     * at each quadrature point.
     */
    double* vecAtQPs;
    WorldVector<double>* gradAtQPs;
    WorldVector<double>* coordsAtQPs;
  
  };


  /**
   * \ingroup Assembler
   *  
   * \brief
   * Laplace operator multiplied with a function evaluated at the quadrature
   * points of a given DOFVector:
   * \f$ -f(v(\vec{x})) \Delta u(\vec{x}) \f$
   */
  class VecAndCoordsAtQP_SOT : public SecondOrderTerm {
  public:
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    /// Constructor.
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    VecAndCoordsAtQP_SOT(DOFVectorBase<double> *dv, 
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			 BinaryAbstractFunction<double, double, WorldVector<double> > *af);
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements SecondOrderTerm::eval().
     */
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    void getLALt(const ElInfo *elInfo, int nPoints, DimMat<double> **LALt) const;    
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

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    void weakEval(int nPoints,
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		  const WorldVector<double> *grdUhAtQP,
		  WorldVector<double> *result) const;

  protected:
    /** \brief
     * DOFVector to be evaluated at quadrature points.
     */
    DOFVectorBase<double>* vec;

    /** \brief
     * Pointer to an array containing the DOFVector evaluated at quadrature
     * points.
     */
    double* vecAtQPs;
  
    WorldVector<double>* coordsAtQPs;

    /** \brief
     * Function evaluated at \ref vecAtQPs.
     */
    BinaryAbstractFunction<double, double,  WorldVector<double> > *f;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * SecondOrderTerm where A is a function which maps the gradient of a 
   * DOFVector at each quadrature point to WorldMatrix<double>:
   * \f$ \nabla \cdot A(\nabla v(\vec{x})) \nabla u(\vec{x})\f$
   */
  class MatrixGradientAndCoords_SOT : public SecondOrderTerm
  {
  public:
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    /// Constructor.
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    MatrixGradientAndCoords_SOT(DOFVectorBase<double> *dv,
				BinaryAbstractFunction<WorldMatrix<double>,
				WorldVector<double> , 
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				WorldVector<double> > *af,
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				AbstractFunction<WorldVector<double>,
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				WorldMatrix<double> > *divAf,
				bool symm = false);
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements SecondOrderTerm::getLALt().
     */
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    void getLALt(const ElInfo *elInfo, int nPoints, DimMat<double> **LALt) const;
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    /** \brief
     * Implenetation of SecondOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

    /** \brief
     * Implenetation of SecondOrderTerm::weakEval().
     */
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    void weakEval(int nPoints,
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		  const WorldVector<double> *grdUhAtQP,
		  WorldVector<double> *result) const;

  protected:
    DOFVectorBase<double>* vec;

    /** \brief
     * Function which maps each entry in \ref gradAtQPs to a WorldMatrix<double>.
     */
    BinaryAbstractFunction<WorldMatrix<double>,
			   WorldVector<double>, WorldVector<double> > *f;

    AbstractFunction<WorldVector<double>, WorldMatrix<double> > *divFct;

    /** \brief
     * Pointer to a WorldVector<double> array containing the gradients of the DOFVector
     * at each quadrature point.
     */
    WorldVector<double>* gradAtQPs;

    WorldVector<double>* coordsAtQPs;

    /** \brief
     * True, if \ref f provides always a symmetric WorldMatrix<double>.
     */
    bool symmetric;
  };

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  class MatrixVec2_SOT : public SecondOrderTerm 
  {
  public:
    /// Constructor.
    MatrixVec2_SOT(DOFVectorBase<double> *dv1, DOFVectorBase<double> *dv2,  
		  BinaryAbstractFunction<double, double, double> *f,
		  WorldMatrix<double> Af,
		  bool sym = false);

    /// Implementation of \ref OperatorTerm::initElement().
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /// Implements SecondOrderTerm::getLALt().
    void getLALt(const ElInfo *elInfo, int nPoints, DimMat<double> **LALt) const;
  
    /// Implenetation of SecondOrderTerm::eval().
    void eval(int nPoints,
	      const double *uhAtQP,
	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

    /// Implenetation of SecondOrderTerm::weakEval().
    void weakEval(int nPoints,
		  const WorldVector<double> *grdUhAtQP,
		  WorldVector<double> *result) const;

  protected:
    /// DOFVector to be evaluated at quadrature points.
    DOFVectorBase<double>* vec1;
    DOFVectorBase<double>* vec2;

    /// Pointer to the values of the DOFVector at quadrature points.
    double* vec1AtQPs;
    double* vec2AtQPs;

    /// Function for A.
    BinaryAbstractFunction<double, double, double> * fct;

    ///
    WorldMatrix<double> A;

    /// True, if \ref matrixFct produces always symmetric matrices.
    bool symmetric;
  };


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  class General_SOT : public SecondOrderTerm
  {
  public:
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    /// Constructor.
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    General_SOT(std::vector<DOFVectorBase<double>*> vecs,
		std::vector<DOFVectorBase<double>*> grads,
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		TertiaryAbstractFunction<WorldMatrix<double>, 
		  WorldVector<double>,
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		  std::vector<double>, 
		  std::vector<WorldVector<double> > > *f,
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		AbstractFunction<WorldVector<double>, 
		  WorldMatrix<double> > *divFct,
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		bool symmetric);
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    /// Implementation of \ref OperatorTerm::initElement().
    void initElement(const ElInfo*, SubAssembler*, Quadrature *quad= NULL);
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    /// Implements SecondOrderTerm::getLALt().
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    void getLALt(const ElInfo *elInfo, int nPoints, DimMat<double> **LALt) const;
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    /// Implenetation of SecondOrderTerm::eval().
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

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    /// Implenetation of SecondOrderTerm::weakEval().
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    void weakEval(int nPoints,
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		  const WorldVector<double> *grdUhAtQP,
		  WorldVector<double> *result) const;

  protected:
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    std::vector<DOFVectorBase<double>*> vecs_; 
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    std::vector<DOFVectorBase<double>*> grads_;
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    TertiaryAbstractFunction<WorldMatrix<double>, 
			     WorldVector<double>,
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			     std::vector<double>, 
			     std::vector<WorldVector<double> > > *f_;
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    AbstractFunction<WorldVector<double>, 
		     WorldMatrix<double> > *divFct_;

    WorldVector<double> *coordsAtQPs_;

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    std::vector<double*> vecsAtQPs_;
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    std::vector<WorldVector<double>*> gradsAtQPs_;
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    bool symmetric_;
  };

  class GeneralParametric_SOT : public SecondOrderTerm
  {
  public:
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    /// Constructor.
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    GeneralParametric_SOT(std::vector<DOFVectorBase<double>*> vecs,
			  std::vector<DOFVectorBase<double>*> grads,
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			  QuartAbstractFunction<WorldMatrix<double>, 
			  WorldVector<double>,
			  WorldVector<double>,
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			  std::vector<double>, 
			  std::vector<WorldVector<double> > > *f,
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			  AbstractFunction<WorldVector<double>, 
			  WorldMatrix<double> > *divFct,
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			  bool symmetric);
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo*, 
		     SubAssembler* ,
		     Quadrature *quad= NULL);

    /** \brief
     * Implements SecondOrderTerm::getLALt().
     */
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    void getLALt(const ElInfo *elInfo, int nPoints, DimMat<double> **LALt) const;
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    /** \brief
     * Implenetation of SecondOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

    /** \brief
     * Implenetation of SecondOrderTerm::weakEval().
     */
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    void weakEval(int nPoints,
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		  const WorldVector<double> *grdUhAtQP,
		  WorldVector<double> *result) const;

  protected:
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    std::vector<DOFVectorBase<double>*> vecs_; 
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    std::vector<DOFVectorBase<double>*> grads_;
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    QuartAbstractFunction<WorldMatrix<double>, 
			  WorldVector<double>,
			  WorldVector<double>,
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			  std::vector<double>, 
			  std::vector<WorldVector<double> > > *f_;
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    AbstractFunction<WorldVector<double>, 
		     WorldMatrix<double> > *divFct_;

    WorldVector<double> *coordsAtQPs_;
    WorldVector<double> elementNormal_;

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    std::vector<double*> vecsAtQPs_;
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    std::vector<WorldVector<double>*> gradsAtQPs_;
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    bool symmetric_;
  };


  // ============================================================================
  // ===== class FirstOrderTerm =================================================
  // ============================================================================

  /**
   * \ingroup Assembler
   * 
   * \brief
   * Describes the first order terms: \f$ b \cdot \nabla u(\vec{x}) \f$
   */
  class FirstOrderTerm : public OperatorTerm
  {
  public:
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    /// Constructor.
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    FirstOrderTerm(int deg) 
      : OperatorTerm(deg) 
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    {}
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    /// Destructor.
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    virtual ~FirstOrderTerm() {}
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    /// Evaluation of \f$ \Lambda b \f$.
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    virtual void getLb(const ElInfo *elInfo,
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		       int nPoints, 
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		       VectorOfFixVecs<DimVec<double> >& result) const = 0;

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    /// Implenetation of FirstOrderTerm::eval().
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    void eval(int nPoints,
	      const double *,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *,
	      double *result,
	      double factor) const 
    {
      int dow = Global::getGeo(WORLD);

      if (grdUhAtQP) {
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	for (int iq = 0; iq < nPoints; iq++) {
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	  double resultQP = 0.0;
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	  for (int i = 0; i < dow; i++)
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	    resultQP += grdUhAtQP[iq][i];
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	  result[iq] += resultQP * factor;
	}
      }
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    }
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  };
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  /**
   * \ingroup Assembler
   *
   * \brief
   * First order term: \f$ b \cdot \nabla u(\vec{x}) \f$ with a vector b which 
   * only consits of entries equal to one.
   */
  class Simple_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
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    Simple_FOT() 
      : FirstOrderTerm(0) 
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    {}
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    /// Implements FirstOrderTerm::getLb().
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    inline void getLb(const ElInfo *elInfo, 
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		      int nPoints, 
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		      VectorOfFixVecs<DimVec<double> >& Lb) const 
    {
      const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();

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      for (int iq = 0; iq < nPoints; iq++)
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	l1(Lambda, Lb[iq], 1.0);
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    }
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  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * First order term: \f$ b \cdot \nabla u(\vec{x}) \f$ with a vector b which 
   * only consits of entries equal to one.
   */
  class FactorSimple_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
    FactorSimple_FOT(double f) 
      : FirstOrderTerm(0)
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    {
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      factor = new double;
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      *factor = f;
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    }
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    /// Constructor.
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    FactorSimple_FOT(double *fptr) 
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      : FirstOrderTerm(0), factor(fptr) 
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    {}
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    /** \brief
     * Implements FirstOrderTerm::getLb().
     */
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    inline void getLb(const ElInfo *elInfo, int nPoints, VectorOfFixVecs<DimVec<double> >& Lb) const
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    {
      const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();

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      for (int iq = 0; iq < nPoints; iq++)
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	l1(Lambda, Lb[iq], (*factor));
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    }
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  private:
    /** \brief
     * Pointer to the factor.
     */
    double *factor;
  };

  /**
   * \ingroup Assembler
   *
   * \brief 
   * First order term: \f$ b \cdot \nabla u(\vec{x}) \f$ with a given vector b.
   */
  class Vector_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
    Vector_FOT(WorldVector<double> wv) 
      : FirstOrderTerm(0), b(wv) 
    {}
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    /// Constructor.
    Vector_FOT(int bIdx) 
      : FirstOrderTerm(0) 
    {
      bOne = bIdx;
    }

    /// Implements FirstOrderTerm::getLb().
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    inline void getLb(const ElInfo *elInfo, 
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		      int nPoints, 
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		      VectorOfFixVecs<DimVec<double> >&Lb) const 
    {
      const DimVec<WorldVector<double> > &Lambda = elInfo->getGrdLambda();

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      if (bOne > -1) {
	for (int iq = 0; iq < nPoints; iq++)
	  lb_one(Lambda, Lb[iq], 1.0);
      } else {
	for (int iq = 0; iq < nPoints; iq++)
	  lb(Lambda, b, Lb[iq], 1.0);
      }
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    }
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    /// Implements FirstOrderTerm::eval().
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    void eval(int nPoints,
	      const double *,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *,
	      double *result,
	      double factor) const
    {
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      if (grdUhAtQP)
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	for (int iq = 0; iq < nPoints; iq++)
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	  result[iq] += b * grdUhAtQP[iq] * factor; 
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    }
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  protected:
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    /// Vector which is multiplied with \f$ \nabla u(\vec{x}) \f$
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    WorldVector<double> b;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * Simple_FOT multiplied with \f$ f(v(\vec{x})) \f$.
   */
  class VecAtQP_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
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    VecAtQP_FOT(DOFVectorBase<double> *dv, 
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		AbstractFunction<double, double> *af,
		WorldVector<double> *wv);
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    /// Constructor.
    VecAtQP_FOT(DOFVectorBase<double> *dv,
		AbstractFunction<double, double> *af,
		int bIdx);

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    /// Implementation of \ref OperatorTerm::initElement().
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    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

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    /// Implements FirstOrderTerm::getLb().
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    void getLb(const ElInfo *elInfo, int nPoints, 
	       VectorOfFixVecs<DimVec<double> >& Lb) const;
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    /// Implements FirstOrderTerm::eval().
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
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    /// DOFVector to be evaluated at quadrature points.
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    DOFVectorBase<double>* vec;

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    /// v at quadrature points.
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    double *vecAtQPs;

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    /// Function f.
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    AbstractFunction<double, double> *f;

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    ///
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    WorldVector<double> *b;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * Simple_FOT multiplied with \f$ f(\vec{x}) \f$.
   */
  class CoordsAtQP_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
    CoordsAtQP_FOT(AbstractFunction<double, WorldVector<double> > *af)
      : FirstOrderTerm(af->getDegree()), g(af) 
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    {}
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements FistOrderTerm::getLb().
     */
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    void getLb(const ElInfo *elInfo, int nPoints,VectorOfFixVecs<DimVec<double> >&Lb) const;
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    /** \brief
     * Implements FirstOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
    /** \brief
     * Stores coordinates at quadrature points. Set in \ref initElement().
     */
    WorldVector<double>* coordsAtQPs;

    /** \brief
     * Function avaluated at world coordinates.
     */
    AbstractFunction<double, WorldVector<double> > *g;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * Vector_FOT multiplied with \f$ f(\vec{x}) \f$.
   */
  class VecCoordsAtQP_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
    VecCoordsAtQP_FOT(AbstractFunction<double, WorldVector<double> > *af,
		      WorldVector<double> wv)
      : FirstOrderTerm(af->getDegree()), g(af), b(wv)
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    {}
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements FistOrderTerm::getLb().
     */
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    void getLb(const ElInfo *elInfo, int nPoints,
	       VectorOfFixVecs<DimVec<double> >& Lb) const;
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    /** \brief
     * Implements FirstOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
    /** \brief
     * Stores coordinates at quadrature points. Set in \ref initElement().
     */
    WorldVector<double>* coordsAtQPs;

    /** \brief
     * Function evaluated at world coordinates.
     */
    AbstractFunction<double, WorldVector<double> > *g;

    /** \brief
     * Coefficient vector.
     */
    WorldVector<double> b;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * First order term: \f$ b(\nabla v(\vec{x})) \cdot \nabla u(\vec{x})\f$.
   */
  class VectorGradient_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
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    VectorGradient_FOT(DOFVectorBase<double> *dv,
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		       AbstractFunction<WorldVector<double>, WorldVector<double> > *af);
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements FirstOrderTerm::getLb().
     */
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    void getLb(const ElInfo *elInfo, int nPoints, 
	       VectorOfFixVecs<DimVec<double> >& Lb) const;
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    /** \brief
     * Implements FirstOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
    DOFVectorBase<double>* vec;

    /** \brief
     * Function for b.
     */
    AbstractFunction<WorldVector<double>, WorldVector<double> > *f;

    /** \brief
     * Gradient of v at quadrature points.
     */
    WorldVector<double> *gradAtQPs;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * First order term: \f$ b(v(\vec{x})) \cdot \nabla u(\vec{x})\f$.
   */
  class VectorFct_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
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    VectorFct_FOT(DOFVectorBase<double> *dv,
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		  AbstractFunction<WorldVector<double>, double> *fct);
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements FirstOrderTerm::getLb().
     */
    void getLb(const ElInfo *elInfo, int qPoint, VectorOfFixVecs<DimVec<double> >& Lb) const; 

    /** \brief
     * Implements FirstOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
    /** \brief
     * DOFVector to be evaluated at quadrature points.
     */
    DOFVectorBase<double>* vec;

    /** \brief
     * Vector v at quadrature points.
     */
    double *vecAtQPs;

    /** \brief
     * Function for b.
     */
    AbstractFunction<WorldVector<double>, double> *vecFct;
  };

  /**
   * \ingroup Assembler
   *
   * \brief
   * 
   */
  class VecFctAtQP_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
    VecFctAtQP_FOT(AbstractFunction<WorldVector<double>, WorldVector<double> > *af)
      : FirstOrderTerm(af->getDegree()), g(af) 
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    {}
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    /** \brief
     * Implementation of \ref OperatorTerm::initElement().
     */
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);

    /** \brief
     * Implements FistOrderTerm::getLb().
     */
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    void getLb(const ElInfo *elInfo, int nPoints,VectorOfFixVecs<DimVec<double> >&Lb) const;
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    /** \brief
     * Implements FirstOrderTerm::eval().
     */
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    void eval(int nPoints,
	      const double *uhAtQP,
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	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
    /** \brief
     * Stores coordinates at quadrature points. Set in \ref initElement().
     */
    WorldVector<double>* coordsAtQPs;

    /** \brief
     * Function avaluated at world coordinates.
     */
    AbstractFunction<WorldVector<double>, WorldVector<double> > *g;
  };

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  /**
   * \ingroup Assembler
   *
   * \brief
   * First order term: \f$ b(v(\vec{x}), \nabla w(\vec{x})) \cdot \nabla u(\vec{x})\f$.
   */
  class VecGrad_FOT : public FirstOrderTerm
  {
  public:
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    /// Constructor.
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    VecGrad_FOT(DOFVectorBase<double> *dv1, DOFVectorBase<double> *dv2,
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		BinaryAbstractFunction<WorldVector<double>, double, WorldVector<double> > *fct);
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    /// Implementation of \ref OperatorTerm::initElement().
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    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);
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    /// Implementation of \ref OperatorTerm::initElement() for multilpe meshes.
    void initElement(const ElInfo* smallElInfo,
		     const ElInfo* largeElInfo,
		     SubAssembler* subAssembler,
		     Quadrature *quad = NULL);
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    /// Implements FirstOrderTerm::getLb().
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    void getLb(const ElInfo *elInfo, int qPoint, 
	       VectorOfFixVecs<DimVec<double> >& Lb) const; 
    
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    /// Implements FirstOrderTerm::eval().
    void eval(int nPoints,
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	      const double *uhAtQP,
	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;
    
  protected:
    /** \brief
     * DOFVector to be evaluated at quadrature points.
     */
    DOFVectorBase<double>* vec1;
    DOFVectorBase<double>* vec2;
    
    /** \brief
     * Vector v at quadrature points.
     */
    double *vecAtQPs;

    WorldVector<double> *gradAtQPs;
    
    /** \brief
     * Function for b.
     */
    BinaryAbstractFunction<WorldVector<double>, double, WorldVector<double> > *vecFct;
  };

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  /**
   * \ingroup Assembler
   *
   * \brief
   * First order term: \f$ b(\nabla v(\vec{x}), \nabla w(\vec{x})) \cdot \nabla u(\vec{x})\f$.
   */
  class FctGrad2_FOT : public FirstOrderTerm
  {
  public:
    /// Constructor
    FctGrad2_FOT(DOFVectorBase<double> *dv1, DOFVectorBase<double> *dv2,
		BinaryAbstractFunction<WorldVector<double>, WorldVector<double>, WorldVector<double> > *vecFct_)
      : FirstOrderTerm(vecFct_->getDegree()), vec1(dv1), vec2(dv2), vecFct(vecFct_) 
    {}

    /// Implementation of \ref OperatorTerm::initElement().
    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);
    
    /// Implements FirstOrderTerm::getLb().
    void getLb(const ElInfo *elInfo, int qPoint, 
	       VectorOfFixVecs<DimVec<double> >& Lb) const; 
    
    /// Implements FirstOrderTerm::eval().
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    void eval(int nPoints,
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	      const double *uhAtQP,
	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;
    
  protected:
    /// DOFVector to be evaluated at quadrature points.
    DOFVectorBase<double>* vec1;

    /// DOFVector to be evaluated at quadrature points.
    DOFVectorBase<double>* vec2;
    
    /// Gradient v at quadrature points.
    WorldVector<double> *grad1AtQPs;

    /// Gradient v at quadrature points.
    WorldVector<double> *grad2AtQPs;

    /// Function for b.
    BinaryAbstractFunction<WorldVector<double>, WorldVector<double>, WorldVector<double> > *vecFct;
  };


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  class Vec2AndGradAtQP_FOT : public FirstOrderTerm
  {
  public:

    Vec2AndGradAtQP_FOT(DOFVectorBase<double> *dv1, 
			DOFVectorBase<double> *dv2,
			TertiaryAbstractFunction<double, double, double, WorldVector<double> > *f_, WorldVector<double> *b_);

    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
		     Quadrature *quad = NULL);
    
    void getLb(const ElInfo *elInfo, int nPoints, VectorOfFixVecs<DimVec<double> >& Lb) const;
    
    void eval(int nPoints,
	      const double              *uhAtQP,
	      const WorldVector<double> *grdUhAtQP,
	      const WorldMatrix<double> *D2UhAtQP,
	      double *result,
	      double factor) const;

  protected:
    DOFVectorBase<double>* vec1;
    DOFVectorBase<double>* vec2;

    double *vec1AtQPs;
    double *vec2AtQPs;  
    WorldVector<double> *gradAtQPs1;

    TertiaryAbstractFunction<double, double, double, WorldVector<double> > *f;
    WorldVector<double> *b;
  };


  class FctVecAtQP_FOT : public FirstOrderTerm
  {
  public:
    FctVecAtQP_FOT(DOFVectorBase<double> *dv,
		   AbstractFunction<double, WorldVector<double> > *f_,
		   WorldVector<double> *b_);
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    void initElement(const ElInfo* elInfo, SubAssembler* subAssembler,
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		     Quadrature *quad = NULL);
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